Problem: Find the greatest common factor of $49$ and $98$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of both $49$ and $98$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}49 &=7\cdot7\\\\\\\\ 98&=2\cdot7\cdot7 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}49 &=7\cdot7\\\\\\\\ 98&=2\cdot7\cdot7 \end{aligned}$ Each number shares the factors ${7}$ and ${7}$, so the GCF is $7\cdot7={49}$. The greatest common factor of $49$ and $98$ is $49$.